Static condensation based reduced order modelling of stochastically parametered large ordered systems

A surrogate stochastic reduced order model is developed for the analysis of randomly parametered structural systems with complex geometries. It is assumed that the mathematical model is available in terms of large ordered finite element (FE) matrices. The structure material properties are assumed to have spatial random inhomogeneities and are modelled as non-Gaussian random fields. A polynomial chaos expansion (PCE) based framework is developed for modelling the random fields directly from measurements and for uncertainty quantification of the response. Difficulties in implementing PCE due to geometrical complexities are circumvented by adopting PCE on a geometrically regular domain that bounds the physical domain and are shown to lead to mathematically equivalent representation. The static condensation technique is subsequently extended for stochastic cases based on PCE formalism to obtain reduced order stochastic FE models. The efficacy of the method is illustrated through two numerical examples.     

Transient waves in composite‐laminated plates with uncertain load and material property

A method is suggested to deal with the wave propagation problems in composite‐laminated plates subjected to uncertainty in load and material property based on the interval analysis method and the hybrid numerical method (HNM). The uncertain parameters are treated as intervals, in which only their bounds of the uncertainty are needed. Using the first‐order Taylor expansion, the transient responses can be approximated as a linear function of the uncertain parameters. In this function, the transient responses at the midpoints of the uncertain parameters can be obtained directly through the HNM. A sensitivity analysis technique is suggested to calculate the first derivative of the transient responses with respect to each uncertain parameter based on two cases that the parameter exists in load or material property. Applying the interval extension in interval mathematics, the lower and upper bounds of the transient responses caused by the uncertainty can be finally obtained. The present method is applied to a numerical example, in which the uncertainty of the load, elastic constants of the layer material and ply orientations are all investigated, and the results demonstrate the effectiveness of the present method. Copyright © 2007 John Wiley & Sons, Ltd.     

Measurement Uncertainty of Dew-Point Temperature in a Two-Pressure Humidity Generator

This article describes the measurement uncertainty evaluation of the dew-point temperature when using a two-pressure humidity generator as a reference standard. The estimation of the dew-point temperature involves the solution of a non-linear equation for which iterative solution techniques, such as the Newton?CRaphson method, are required. Previous studies have already been carried out using the GUM method and the Monte Carlo method but have not discussed the impact of the approximate numerical method used to provide the temperature estimation. One of the aims of this article is to take this approximation into account. Following the guidelines presented in the GUM Supplement 1, two alternative approaches can be developed: the forward measurement uncertainty propagation by the Monte Carlo method when using the Newton?CRaphson numerical procedure; and the inverse measurement uncertainty propagation by Bayesian inference, based on prior available information regarding the usual dispersion of values obtained by the calibration process. The measurement uncertainties obtained using these two methods can be compared with previous results. Other relevant issues concerning this research are the broad application to measurements that require hygrometric conditions obtained from two-pressure humidity generators and, also, the ability to provide a solution that can be applied to similar iterative models. The research also studied the factors influencing both the use of the Monte Carlo method (such as the seed value and the convergence parameter) and the inverse uncertainty propagation using Bayesian inference (such as the pre-assigned tolerance, prior estimate, and standard deviation) in terms of their accuracy and adequacy.     

Development of stochastic isogeometric analysis (SIGA) method for uncertainty in shape

In this paper, a new method is proposed that extend the classical deterministic isogeometric analysis (IGA) into a probabilistic analytical framework in order to evaluate the uncertainty in shape and aim to investigate a possible extension of IGA in the field of computational stochastic mechanics. Stochastic IGA (SIGA) method for uncertainty in shape is developed by employing the geometric characteristics of the non-uniform rational basis spline and the probability characteristics of polynomial chaos expansions (PCE). The proposed method can accurately and freely evaluate problems of uncertainty in shape caused by deformation of the structural model. Additionally, we use the intrusive formulation approach to incorporate PCE into the IGA framework, and the C++ programming language to implement this analysis procedure. To verify the validity and applicability of the proposed method, two numerical examples are presented. The validity and accuracy of the results are assessed by comparing them to the results obtained by Monte Carlo simulation based on the IGA algorithm.     

Uncertainty considerations in AC loss measurement of multifilamentary superconducting wires performed via a pickup coil method

The uncertainty of AC loss measurements for multifilamentary superconducting wires by a pickup coil method is evaluated on the basis of the law of propagation of uncertainty. In this evaluation, the effects of measurement conditions, signal processing, and the division of the AC loss into its components (hysteresis loss and coupling loss) are taken into account as elements of uncertainty. The effect of the measurement conditions is evaluated using theoretical expressions of the two main components. Additionally, the effect of signal processing is considered in accordance with the actual processes of the AC loss measurement using experimental outputs. The main factors that contribute to the uncertainty in the propagation process are discussed. The estimated resultant uncertainties are compared to experimental ones for round robin tests of AC loss measurement of Nb-Ti multifilamentary wires exposed to an alternating transverse magnetic field.     

PCE/POM/EVA共混体系高强高韧化的研究

对PCE/POM、PCE/EVA、PCE/POM/EVA三种共混体系的物理机械性能进行了研究和对比。通过分析表明,EVA对PCE/POM共混体系有增容作用,POM对PCE/EVA共混体系有增强作用,从而开发出一种强韧的聚氯醚合金。      

Sparse polynomial chaos expansions of frequency response functions using stochastic frequency transformation

Frequency response functions (FRFs) are important for assessing the behavior of stochastic linear dynamic systems. For large systems, their evaluations are time-consuming even for a single simulation. In such cases, uncertainty quantification by crude Monte-Carlo simulation is not feasible. In this paper, we propose the use of sparse adaptive polynomial chaos expansions (PCE) as a surrogate of the full model. To overcome known limitations of PCE when applied to FRF simulation, we propose a frequency transformation strategy that maximizes the similarity between FRFs prior to the calculation of the PCE surrogate. This strategy results in lower-order PCEs for each frequency. Principal component analysis is then employed to reduce the number of random outputs. The proposed approach is applied to two case studies: a simple 2-DOF system and a 6-DOF system with 16 random inputs. The accuracy assessment of the results indicates that the proposed approach can predict single FRFs accurately. Besides, it is shown that the first two moments of the FRFs obtained by the PCE converge to the reference results faster than with the Monte-Carlo (MC) methods.     

The use of a Monte Carlo method for uncertainty calculation, with an application to the measurement of neutron ambient dose equivalent rate

This paper is concerned with the use of a Monte Carlo method for uncertainty calculation as an implementation of the propagation of distributions. It reviews the basic principles of the propagation of distributions and numerical aspects of a Monte Carlo implementation. It also discusses the possible advantages in some circumstances of the propagation of distributions over the GUM uncertainty framework, and how the results obtained in any particular instance can be compared with those provided by that framework. To illustrate these various aspects, an application to the measurement of neutron dose equivalent rate is given. A key consideration in this application is the manner in which the dominant source of uncertainty, namely that associated with the field-specific correction factor, is treated. The information available concerning this factor constitutes the correction factors for a set of fields of the same type as that in which a measurement is being made. This information is encoded as a probability density function (PDF) for the correction factor. This PDF constitutes an input to both methods of evaluation.     

Uncertainty and Worst-Case Analysis in Electrical Measurements Using Polynomial Chaos Theory

In this paper, the authors propose an analytical method for estimating the possible worst-case measurement due to the propagation of uncertainty. This analytical method uses polynomial chaos theory (PCT) to formally include the effects of uncertainty as it propagates through an indirect measurement. The main assumption is that an analytical model of the measurement process is available. To demonstrate the use of PCT to assess a worst-case measurement, the authors present two examples. The first one involves the use of PCT to estimate the possible worst case of a measurement due to the propagation of parametric uncertainty of a low-pass filter. This case study concerns the analysis of nonlinear effects on the propagation of uncertainty of a signal-conditioning stage used in power measurement. In this paper, the PCT method is applied to determine the probability density function (pdf) of magnitude and phase of the frequency response of the filter and their impact on the power measurement. Of particular interest is the use of PCT to determine the worst-case, expected-case, and best-case effects of the filter, avoiding the reconstruction of the complete pdf of the filter output. The results illustrate the potential of this method to determine the significant boundary of measurement uncertainty, even when the uncertainty propagates through a nonlinear nonpolynomial function. In the second example, the authors use PCT to perform a worst-case analysis for an indirect measurement of a loop impedance. For both examples, the PCT method is compared with the numerical Monte Carlo analysis and the analytical method described in the guide on uncertainty on measurements (GUM).      

Reliability analysis for multidisciplinary systems with the mixture of epistemic and aleatory uncertainties

Epistemic and aleatory uncertain variables always exist in multidisciplinary system simultaneously and can be modeled by probability and evidence theories, respectively. The propagation of uncertainty through coupled subsystem and the strong nonlinearity of the multidisciplinary system make the reliability analysis difficult and computational cost expensive. In this paper, a novel reliability analysis procedure is proposed for multidisciplinary system with epistemic and aleatory uncertain variables. First, the probability density function of the aleatory variables is assumed piecewise uniform distribution based on Bayes method, and approximate most probability point is solved by equivalent normalization method. Then, important sampling method is used to calculate failure probability and its variance and variation coefficient. The effectiveness of the procedure is demonstrated by two numerical examples. Copyright © 2013 John Wiley & Sons, Ltd.     

A Combined Sensitive Matrix Method and Maximum Likelihood Method for Uncertainty Inverse Problems

The uncertainty inverse problems with insufficiency and imprecision in the input and/or output parameters are widely existing and unsolved in the practical engineering. The insufficiency refers to the partly known parameters in the input and/or output, and the imprecision refers to the measurement errors of these ones. In this paper, a combined method is proposed to deal with such problems. In this method, the imprecision of these known parameters can be described by probability distribution with a certain mean value and variance. Sensitive matrix method is first used to transform the insufficient formulation in the input and/or output to a resolvable one, and then the mean values of these unknown parameters can be identified by maximizing the likelihood of the measurements. Finally, to quantify the uncertainty propagation, confidence intervals of the obtained solutions are calculated based on linearization and Monte Carlo methods. Two numerical examples are presented to demonstrate the effectiveness of the present method.     

Robust topology optimization of continuum structures with loading uncertainty using a perturbation method

An approach for the robust topology optimization (RTO) of continuum structures with loading uncertainty is investigated. The loading uncertainties are quantified using the second order Taylor series expansion of uncertain loading magnitudes and directions, and then the response statistic mean and standard deviation of compliance are calculated using the uncertain perturbation propagation method. A robust design Lagrange function considering the compliance objective and finite element constraints is developed, and a sensitivity analysis is performed to calculate the Lagrange coefficients. The Lagrange objective function is optimized using the modified solid isotropic material with penalization (SIMP) algorithm; thus, the optimum material distribution under loading uncertainty is acquired. The proposed methodology is used for the RTO of two examples, revealing its efficiency under both concentrated and distributed uncertain loadings. The accuracy of the results is verified by comparison with similar cases found in the literature where a different modelling approach was used.     

Hierarchical surrogate model with dimensionality reduction technique for high-dimensional uncertainty propagation

In this article, hierarchical surrogate model combined with dimensionality reduction technique is investigated for uncertainty propagation of high-dimensional problems. In the proposed method, a low-fidelity sparse polynomial chaos expansion model is first constructed to capture the global trend of model response and exploit a low-dimensional active subspace (AS). Then a high-fidelity (HF) stochastic Kriging model is built on the reduced space by mapping the original high-dimensional input onto the identified AS. The effective dimensionality of the AS is estimated by maximum likelihood estimation technique. Finally, an accurate HF surrogate model is obtained for uncertainty propagation of high-dimensional stochastic problems. The proposed method is validated by two challenging high-dimensional stochastic examples, and the results demonstrate that our method is effective for high-dimensional uncertainty propagation.     

Robust topology optimization for cellular composites with hybrid uncertainties

This paper will develop a new robust topology optimization method for the concurrent design of cellular composites with an array of identical microstructures subject to random‐interval hybrid uncertainties. A concurrent topology optimization framework is formulated to optimize both the composite macrostructure and the material microstructure. The robust objective function is defined based on the interval mean and interval variance of the corresponding objective function. A new uncertain propagation approach, termed as a hybrid univariate dimension reduction method, is proposed to estimate the interval mean and variance. The sensitivity information of the robust objective function can be obtained after the uncertainty analysis. Several numerical examples are used to validate the effectiveness of the proposed robust topology optimization method.     

基于频响函数综合的浮筏隔振系统误差传递分析

采用基于频响函数综合的子结构方法对浮筏隔振系统进行建模分析和误差传递分析。针对测试频响函数的一些常见误差,如测试噪声对频响函数幅值和相位的污染,同一子结构的频响函数不满足互易性,原点频响函数的虚部小于零等,分析其在综合时由于误差传递和放大效应对综合结果的影响。并采用矩方法对误差传递进行定量分析,将矩方法的结果和采用Monte Carlo方法的结果进行对比,结果表明矩方法具有较高的效率和精度。     

基于多项式混沌理论的不确定度评定与分析

针对基于ISO GUM提供的测量不确定度评估方法所存在的局限,提出了采用多项式混沌方法进行测量结果不确定度评估的新方法。分析了GUM测量不确定度评估方法所隐含的假设条件,给出了多项式混沌方法的测量不确定度评估原理。通过GUM与多项式混沌方法扩展不确定度包含因子估计误差的数值计算表明,当随机变量的PDF不满足高斯分布时,多项式混沌估计方法所获得的扩展不确定度更能反映实际情况。     

The effect of ionic strength and hardness of water on the non-ionic surfactant-enhanced remediation of perchloroethylene contamination

The objective of this study is to evaluate the perchloroethylene (PCE) removal by an aqueous surfactant solutions based on influential factors (ionic strength, hardness) of various groundwaters and surface waters contaminated with PCE. The experimental methods used in this study were separatory funnel experiments and batch experiments. Separatory funnel experiments were performed to determine which surfactants are good solubilizers for PCE. Batch experiments were performed to evaluate the effect of ions in sampled water for PCE removal. The results of separatory funnel experiments indicated that the surfactant polyoxyethylene (20) sorbitan monostearate (Tween 60) showed to be a predominant solubilizer for the removal of PCE (87.3%). Separatory funnel experiments also showed that the hydrophilic-lipophilic balance (HLB) number and the chemical structure of the surfactants were good indicators of surfactant effectiveness for removal of PCE from water. The results of batch experiments showed that non-ionic surfactants are affected by the ionic strength of sampled water. The % of PCE removal of the Tween 60 surfactant solution was measured to be 88.3% by batch experiments. This result was affected by the characteristics of the surfactant (HLB, chemical structures) and the ionic strength of water. Therefore, the ionic strength of contaminated water, HLB and chemical structures of surfactants must be considered in surfactant-enhanced remediation.     

少量声速剖面时浅海声传播不确定性研究

当只有少量的浅海实测声速剖面时,不能直接利用Monte Carlo法研究声传播的不确定性。基于经验正交函数法,提出扩展向量法对少量实测声速剖面进行扩展,产生与实测声速剖面统计量基本一致的扩展声速剖面,基于MonteCarlo法,利用扩展后的声速剖面计算了声传播损失概率密度分布。结果表明,扩展向量元素服从标准正态分布,扩展后的数据捕捉到了未能测量到、但可能存在的声速剖面,该方法为浅海环境下实测声速剖面数据较少时,研究声传播不确定性提供了一种新的途径。     

High‐Efficiency Nonfullerene Organic Solar Cells with a Parallel Tandem Configuration

In this work, a highly efficient parallel connected tandem solar cell utilizing a nonfullerene acceptor is demonstrated. Guided by optical simulation, each of the active layer thicknesses of subcells are tuned to maximize its light trapping without spending intense effort to match photocurrent. Interestingly, a strong optical microcavity with dual oscillation centers is formed in a back subcell, which further enhances light absorption. The parallel tandem device shows an improved photon‐to‐electron response over the range between 450 and 800 nm, and a high short‐circuit current density (J _SC) of 17.92 mA cm^?2. In addition, the subcells show high fill factors due to reduced recombination loss under diluted light intensity. These merits enable an overall power conversion efficiency (PCE) of >10% for this tandem cell, which represents a ≈15% enhancement compared to the optimal single‐junction device. Further application of the designed parallel tandem configuration to more efficient single‐junction cells enable a PCE of >11%, which is the highest efficiency among all parallel connected organic solar cells (OSCs). This work stresses the importance of employing a parallel tandem configuration for achieving efficient light harvesting in nonfullerene‐based OSCs. It provides a useful strategy for exploring the ultimate performance of organic solar cells.     

Galerkin based generalized ANOVA for the solution of stochastic steady state diffusion problems

This work presents a novel approach, referred here as Galerkin based generalized analysis of variance decomposition (GG-ANOVA), for the solution of stochastic steady state diffusion problems. The proposed approach utilizes generalized ANOVA (G-ANOVA) expansion to represent the unknown stochastic response and Galerkin projection to decompose the stochastic differential equation into a set of coupled differential equations. The coupled set of partial differential equations obtained are solved using finite difference method and homotopy algorithm. Implementation of the proposed approach for solving stochastic steady state diffusion problems has been illustrated with three numerical examples. For all the examples, results obtained are in excellent agreement with the benchmark solutions. Additionally, for the second and third problems, results obtained have also been compared with those obtained using polynomial chaos expansion (PCE) and conventional G-ANOVA. It is observed that the proposed approach yields highly accurate result outperforming both PCE and G-ANOVA. Moreover, computational time required using GG-ANOVA is in close proximity of G-ANOVA and less as compared to PCE.